The emergence of functional specialization is a core problem in biology. In this work we focus on the emergence of reproductive (germ) and vegetative viability-enhancing (soma) cell functions (or germ-soma specialization). We consider a group of cells and assume that they contribute to two different evolutionary tasks, fecundity and viability. The potential of cells to contribute to fitness components is traded off. As embodied in current models, the curvature of the trade-off between fecundity and viability is concave in small-sized organisms and convex in large-sized multicellular organisms. We present a general mathematical model that explores how the division of labor in a cell colony depends on the trade-off curvatures, a resource constraint and different fecundity and viability rates. Moreover, we consider the case of different trade-off functions for different cells. We describe the set of all possible solutions of the formulated mathematical programming problem and show some interesting examples of optimal specialization strategies found for our objective fitness function. Our results suggest that the transition to specialized organisms can be achieved in several ways. The evolution of Volvocalean green algae is considered to illustrate the application of our model. The proposed model can be generalized to address a number of important biological issues, including the evolution of specialized enzymes and the emergence of complex organs.
